Well, I have paired my Alt8 in an Alder bodied supestrat with a maple top with a Suhr Doug Aldrich which, to my ears sounds the closest to, you guessed it, a bit hotter Jazz.
TBH I haven't tried a jazz bridge in the neck but that'd be a good place to start if you want a bit more output. Otherwise the usual JazzN is a pretty great pickup and IMO, sounds a lot better than the '59 which I always found to be too warm and undefined.
Warmoth 'Les Paul' - BraveheartI've got a JazzN with my Alt8 - the construction and materials are somewhat different to your V though
Warmoth 'Les Paul' - Braveheart
Jazz